Question
The maximum value attained by the function \(f\left( x \right) = x\left( {x - 1} \right)\left( {x - 2} \right)\) in the interval [1, 2] is _____.
\(f\left( x \right) = x\left( {x - 1} \right)\left( {x - 2} \right)\)
At x = 0, f(x) = 0
At any value of x between 0 and 1, f(x) is positive.
At x = 1, f(x) = 0
At any value of x between 1 and 2, f(x) is negative.
At x = 2, f(x) = 0
The curve for \(f\left( x \right) = x\;\left( {x-1} \right)\;\left( {x-2} \right)\) will approximately be
Therefore, in the given interval [1, 2], the maximum value of f(x) is 0.
Was this answer helpful?
Important Questions from Maxima & Minima
The function ƒ(x) = 3x (x - 2) has:
- The minimum value of the function $f(x) = |x| + |2x + 3|$ for real $x$ is ________ (rounded off to 1 decimal place).
- The value of the determinant of the Hessian of $f(x,y) = x^2 + y^2 + xy - 8x - 7y$ at its stationary point is
- A rectangular box with an open top has an outer surface area of 12 m$^2$. The length of the base is twice the width. If the volume of the box is to be maximised, then the ratio of length to height should be ____________. (answer in integer)
- A wire of length $L$ is cut into two pieces to construct a circle and an equilateral triangle such that the combined area is minimum. The length of the wire used to construct the circle is
Need Expert Advice?
